0dd4cf9155857c8b272461e36f6f6b27 mathematics-13-00091.pdf 02176aa410d80ad46e02b0801531cc2ccef86a28 mathematics-13-00091.pdf 3f306c2a677500bb61e2a59e3c0efa319d0421fc015dba79973dec430705af16 mathematics-13-00091.pdf Title: A Paradigm for Modeling Infectious Diseases: Assessing Malware Spread in Early-Stage Outbreaks Subject: As digitalization and artificial intelligence advance, cybersecurity threats intensify, making malware—a type of software installed without authorization to harm users—an increasingly urgent concern. Due to malware’s social and economic impacts, accurately modeling its spread has become essential. While diverse models exist for malware propagation, their selection tends to be intuitive, often overlooking the unique aspects of digital environments. Key model choices include deterministic vs. stochastic, planar vs. spatial, analytical vs. simulation-based, and compartment-based vs. individual state-tracking models. In this context, our study assesses fundamental infection spread models to determine those most applicable to malware propagation. It is organized in two parts: the first examines principles of deterministic and stochastic infection models, and the second provides a comparative analysis to evaluate model suitability. Key criteria include scalability, robustness, complexity, workload, transparency, and manageability. Using consistent initial conditions, control examples are analyzed through Python-based numerical methods and agent-based simulations in NetLogo. The findings yield practical insights and recommendations, offering valuable guidance for researchers and cybersecurity professionals in applying epidemiological models to malware spread. Keywords: epidemiological models; mathematical modeling; malware spread modeling; sociotechnical systems; simulation Author: Egils Ginters, Uga Dumpis, Laura Calvet Liñán, Miquel Angel Piera Eroles, Kawa Nazemi, Andrejs Matvejevs and Mario Arturo Ruiz Estrada Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Sun Dec 29 10:12:03 2024 CET ModDate: Sun Dec 29 10:15:14 2024 CET Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 35 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 7812477 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- AIQCCL+VnURWPalladioL-Bold Type 1 Custom yes yes yes 10 0 BIIZJQ+URWPalladioL-Roma Type 1 Custom yes yes yes 16 0 RYPWTV+URWPalladioL-Bold Type 1 Custom yes yes yes 22 0 KNYTCJ+URWPalladioL-Ital Type 1 Custom yes yes yes 27 0 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Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Methodology Destination: section.2 Children: Item: Title: The Conceptual Model of the Spread of Infections Destination: subsection.2.1 Item: Title: The SIR Model A Basic Approach to Contagion Modeling Destination: subsection.2.2 Item: Title: The SIR Model with Vital Dynamics Destination: subsection.2.3 Item: Title: The SIS Model for Describing Recurrent Infection Dynamics Destination: subsection.2.4 Item: Title: The SIR Model with Vaccination and Mutations Destination: subsection.2.5 Item: Title: Incorporating Diffusion Dynamics in the SIR Model Destination: subsection.2.6 Item: Title: Stochastic SIR Model Introducing Noise to Deterministic Dynamics Destination: subsection.2.7 Item: Title: Network Model Tracking Compartment Changes via Individual Status Destination: subsection.2.8 Children: Item: Title: Graph-Based Models Destination: subsubsection.2.8.1 Item: Title: ABM for Network Simulation Destination: subsubsection.2.8.2 Item: Title: Results Destination: section.3 Children: Item: Title: Application Results of the Classic SIR Model Destination: subsection.3.1 Item: Title: Modeling Outcomes for the SIR Model with Vital Dynamics Destination: subsection.3.2 Item: Title: Results from Applying the SIS Model Destination: subsection.3.3 Item: Title: SIR Model Results: Vaccination and Mutation Effects Destination: subsection.3.4 Item: Title: Evaluation of SIR Model Results with Diffusion Destination: subsection.3.5 Item: Title: Findings from the Stochastic SIR Model Destination: subsection.3.6 Item: Title: Implementing Network SIR Models Destination: subsection.3.7 Children: Item: Title: Graph Theory Application in Network Modeling Destination: subsubsection.3.7.1 Item: Title: SIR ABM Model Simulation Results Destination: subsubsection.3.7.2 Item: Title: Discussion Destination: section.4 Item: Title: Conclusions Destination: section.5 Item: Title: References Destination: section.6 Info: Title: A Paradigm for Modeling Infectious Diseases: Assessing Malware Spread in Early-Stage Outbreaks Author: Egils Ginters, Uga Dumpis, Laura Calvet Liñán, Miquel Angel Piera Eroles, Kawa Nazemi, Andrejs Matvejevs and Mario Arturo Ruiz Estrada Subject: As digitalization and artificial intelligence advance, cybersecurity threats intensify, making malware a type of software installed without authorization to harm users an increasingly urgent concern. Due to malware’s social and economic impacts, accurately modeling its spread has become essential. While diverse models exist for malware propagation, their selection tends to be intuitive, often overlooking the unique aspects of digital environments. Key model choices include deterministic vs. stochastic, planar vs. spatial, analytical vs. simulation-based, and compartment-based vs. individual state-tracking models. In this context, our study assesses fundamental infection spread models to determine those most applicable to malware propagation. It is organized in two parts: the first examines principles of deterministic and stochastic infection models, and the second provides a comparative analysis to evaluate model suitability. Key criteria include scalability, robustness, complexity, workload, transparency, and manageability. Using consistent initial conditions, control examples are analyzed through Python-based numerical methods and agent-based simulations in NetLogo. The findings yield practical insights and recommendations, offering valuable guidance for researchers and cybersecurity professionals in applying epidemiological models to malware spread. 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